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Solutions
The correct sequence is: BFDCEGA
The central idea of the passage relates to Afghanistan's raising of 7000 security personnel to guard the TAPI pipeline. Thus, sentence B is the opening sentence of the series. What should follow this announcement logically is, India heaving a sigh of relief, given she has a number of projects at stake due to the threat of terrorism. Thus, sentence F should follow B.
C and D form a mandatory pair, given both the sentences talk about the same person, i.e., about the petroleum ministers' statement, and are in continuation. D will precede C as sentence D states the minister's name and sentence C starts with the pronoun 'he' and continues with his statement regarding the project.
Statement E should follow statement C because the latter ends saying that the project will begin in April, so what should follow is the course of action to be taken after the project begins.
Statement E talks about the challenge to be faced as a result of laying of the pipeline.
Statement G builds on the argument of the official as is exemplified by the use of 'further', and hence, should come after statement E. Also, statement E mentions Afghanistan and Pakistan as the two major countries via which the pipeline would pass and statement G uses the word 'each host country', thus, making G and E a mandatory pair with E preceding G.
What is left is statement A which gives us a larger picture as a result of laying this pipeline which includes the meeting of the energy needs along with improving bilateral relations.